Severe problems of congestion and delay have existed in both criminal and civil courts throughout the country for many years. Only in the last few years, however, have the techniques of operations research been applied to the effective administration of these courts. These applications are of two primary types: the allocation of court and related resources, and the scheduling of case appearances. This paper summarizes some recent work in the development of the quantitative models that form the basis of such applications, introduces an original model, and suggests promising areas for further work of this type. The models discussed include analytic and simulation models of case flow, scheduling, and courtroom activities. 31 pp. Ref.